no. 4
Homological algebra/Topology
Hochschild cohomology of poset algebras and Steenrod operations
[La cohomologie de Hochschild des algèbres posets et les opérations de Steenrod]

Présenté par : the Editorial Board

Lodder, Jerry1
1 Mathematical Sciences, Dept. 3MB, New Mexico State University, Las Cruces, NM 88003, USA
Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 339-343.

On démontre que l'isomorphisme de la cohomologie de Hochschild d'une algèbre poset A à la cohomologie simpliciale du classifiant de la catégorie associé à A applique le produit pré-Lie de Gerstenhaber au produit cup-one de Steenrod. Sur les cochaînes, cette application devient un isomorphisme des algèbres différentielles graduées commutatives à homotopie près.

We show that the isomorphism from the Hochschild cohomology of a poset algebra A to the simplicial cohomology of the classifying space of the category associated with A maps Gerstenhaber's pre-Lie product to Steenrod's cup-one product. On cochains, this map becomes an isomorphism of differential graded homotopy commutative algebras.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.01.003
Lodder, Jerry 1

1 Mathematical Sciences, Dept. 3MB, New Mexico State University, Las Cruces, NM 88003, USA 
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Lodder, Jerry. Hochschild cohomology of poset algebras and Steenrod operations. Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 339-343. doi : 10.1016/j.crma.2016.01.003. http://www.numdam.org/articles/10.1016/j.crma.2016.01.003/

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